Don't worry too much about kana. It feels impossible now but it will become second nature. At some point you will hate it when someone uses romaji since kana is so much easier to read.
I do remember using the "Remembering the Kana" book: http://www.amazon.co.jp/Remembering-Kana-The-Hiragana-Kataka... which I can recommend 100%. The 3 hours claim is accurate from what I remember but do follow the book's suggested breaks.
But it's not just triplets. You can have 2, 3, or 4 components per character (Wikipedia says 5, but I'm not sure how that works). The first component must be a consonant, but there's a null consonant too, allowing you to create syllables with just a vowel sound.
I don't see how the writing system itself helps typists. If words are shorter, that's a function of shorter words, not the writing system. A syllable still requires several keystrokes each.
That said, it's very simple to learn. I learned it in a week. But, I also learned the Japanese scripts (hiragana/katakana) in a week as well using James Heisig's awesome book. So, perhaps learning alphabet scripts is just not an overly difficult task in general?
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